Read the fictional model boundaries
Assume fixed certain payments, compatible positive factors, annual dates and no trading costs. The problems concern mathematical consistency, not a real issuer trade. Keep the final coupon separate from principal while forming the total final receipt.
Write the price equation before the answer
For bootstrapping, subtract the already known coupon value before solving the final factor. For a future valuation date, divide the payment factor by the factor of that date. For a local node change, trace the affected payment rather than assuming every horizon shifted.
Try the questions
D1 = 0.96. A two-year bond paying 5 then 105 costs 99. What is D2?
- A.
0.942857
- B.
0.897143
- C.
0.99
Answer and explanation
Answer: B
99 = 5×0.96 + 105D2. The known first coupon is valued before isolating D2.
- A
99/105 ignores the year-one coupon.
- B
Subtract 5×0.96, then divide by 105.
- C
99/100 ignores both the coupon schedule and the final coupon.
A single amount X is due at year three. Which expression gives its curve-implied value at year one?
- A.
X D3 D1
- B.
X D3 / D1
- C.
X / D3
Answer and explanation
Answer: B
Multiplying that year-one value by D1 returns today’s value XD3.
- A
Multiplication discounts to today and then earlier again.
- B
The ratio converts the payment to the year-one valuation date.
- C
This accumulates rather than discounts the future payment.
Only the two-year spot node changes in a model with payments exactly at years one, two and three. The other spot nodes are held fixed. Which statement follows?
- A.
All three payment PVs must change
- B.
Only the year-two payment PV changes directly
- C.
The terminal principal automatically uses the two-year rate
Answer and explanation
Answer: B
This is the explicit independent-node model, not a broader interpolated key-rate shock.
- A
That describes a different scenario from the specified fixed-node map.
- B
Each payment uses its own dated spot factor.
- C
The year-three principal uses the year-three factor.